"No scientific evidence this product works" will be ignored. "This product does not work" would be more effective.
It's better to make the negative claim (the former) rather than risk losing what little authority you have with people who are struggling to understand the evidence behind these products to begin with.
Which is to say, we're not 100% sure it's bullshit—we can't be, in science—but we're 99.999999% sure, or so.
However, if a label would say "10 peer reviewed and published scientific studies find no evidence that this product works". Now that is convincing.
"No scientific evidence this product works" does not mean the same thing as "this product does not work!" People confusing the two is very harmful.
It could mean, for example, "there is plausible mechanism of action but there hasn't been much research on the topic [for whatever reason]" or it could mean "there's absolutely no known mechanism of action, it doesn't make physiological sense, and a century of research has proved it doesn't work." These two statements are obviously not the same!
> However, if a label would say "10 peer reviewed and published scientific studies find no evidence that this product works". Now that is convincing.
I don't think that this is how medical labelling should work. If you want to sell a product on the basis of its effect on your health, then the onus should be on you to prove that it works, not on others to prove that it doesn't. In this setting, I think that a presumption of guilt (ineffectiveness or harmfulness) until proven otherwise is appropriate.
The fundamental problem I think is that much of society simply doesn't understand what science is, and why it's important, or why they should care about scientific studies in regard to allegedly medicinal products they may use.
The rest of the placebo effect, outside of that domain, is being increasingly found to be the result of under-powered experiments.
To show something only has a placebo effect is the equivalent of showing it does not work.
The (understandable, traditional) reason for measuring relative to placebo is that, "well, you don't need the drug if it's only as good as what a placebo gives -- just use the cheaper placebo! You should only bother with some special drug if it's better than what mere belief-in-effectiveness yields."
But that assumes that people are equally credulous of every placebo; if a person is more credulous of homeopathy, and credulity is hard to manufacture, then it's not quite wrong to say that it "works" under a relevant definition.
(I know this is kind of an angels-on-the-head-of-a-pen technicality, but eventually we'll want to actually understand why belief-in-effectiveness can matter at all, so we can exploit it, and reasoning like yours tends to give the idea that such an effort, by definition, can't work.)